Title: Lattice minors and Eulerian posets

 
Abstract: We define a notion of deletion and contraction for lattices. The result of a sequence of deletions and contractions is called a minor of the original lattice. The name minors is justified by the fact that the minors of the lattice of flats of a graph correspond to the simple minors of the graph when the vertices are labeled (and the edges unlabeled). For each finite lattice we define a poset of minors and show it is Eulerian and a PL sphere. We also obtain some inequalities for the cd-indices of these posets of minors.